NIKISHINE, Ukraine/BUDAPEST, Feb 17 (Reuters) - Russian
President Vladimir Putin told Kiev to let its soldiers surrender
to pro-Russian rebels, who spurned a ceasefire in eastern
Ukraine and fought their way on Tuesday into the town of
Debaltseve, encircling thousands of government troops.

A peace deal reached at all-night talks in the Belarussian
capital Minsk last week had all but unravelled, with both sides
failing to begin pulling back heavy guns as required after the
rebels refused to halt their advance.

Putin, whom Western countries accuse of directing the rebel
assault with Russian soldiers and weapons, said Kiev should
allow its soldiers to surrender to the advancing rebels.

"I hope that the responsible figures in the Ukrainian
leadership will not hinder soldiers in the Ukrainian army from
putting down their weapons," Putin said.

"If they aren't capable of taking that decision themselves
and giving that order, then (I hope) that they won't prosecute
people who want to save their lives and the lives of others."

He added that he hoped the rebels would allow the Ukrainians
to return to their families, once they had surrendered the town.

Reuters journalists near the snowbound frontline said
artillery rounds were rocking Debaltseve every five seconds and
black smoke was rising skywards as Grad rockets pounded the
town.

The rebels say the ceasefire announced last week does not
apply at all to the main battle front at Debaltseve, a railway
hub in a pocket between the two main rebel-held areas.

"SURRENDER TALKS"

"Eighty percent of Debaltseve is already ours," said Eduard
Basurin, a rebel leader. "A clean-up of the town is under way."

He later said negotiations were under way for 5,000
Ukrainian troops to surrender. "Hundreds" had been captured and
would eventually be released to their families. Ukraine denied
that the number of captives was that high.

Despite Putin's public call for a surrender, Russia
sponsored a resolution adopted by the U.N. Security Council that
called on all sides to implement the truce agreement, expressing
"grave concern" at the violence.

Putin was visiting Hungary on Tuesday, his first bilateral
trip to an EU country since last July, when Moscow was left
isolated after a Malaysian airliner was shot down over
rebel-held territory with what Western countries say was a
Russian-supplied missile.

Hopes that the deal reached last Thursday would end a
conflict that has killed more than 5,000 people were always low
after a rebel advance in January ended an earlier truce.

But Western countries appeared surprised that the rebels had
refused even to pay lip service to the ceasefire at Debaltseve.

Russia has already annexed Ukraine's Crimean Peninsula, and
Western countries believe Putin's goal is to establish a "frozen
conflict" in eastern Ukraine, gaining permanent leverage over a
country of 45 million people seeking integration with Europe.

Ukrainian President Petro Poroshenko called the rebel
assault on the town a cynical attack on the Minsk agreement.

U.S. "GRAVELY CONCERNED"

Kiev's military denied that the town, which had a peacetime
population of 25,000 but is now a bombed-out wasteland, had
fallen, but acknowledged losing some of it.

Kiev and NATO say the rebel assault on Debaltseve is being
reinforced by Russian tanks, artillery and soldiers. Moscow
denies that it has sent its forces to participate in the battle
for a region that Putin has dubbed "New Russia".

Washington said it was "gravely concerned" by the fighting
and was monitoring reports of a new column of Russian military
equipment heading to the area.

The United States has been considering sending weapons to
aid Kiev, although the State Department said on Tuesday getting
into a proxy war with Russia was not in the interests of Ukraine
or the world. Putin said he believed foreign weapons were
already being supplied to Kiev.

EU foreign policy chief Francesca Mogherini said Tuesday's
battles were "not encouraging" but added: "As long as there is a
signed deal to which the parties still refer as something that
needs to be implemented, I will not say that there is a
failure."

The fighting meant both sides had spurned Tuesday's deadline
to being withdrawing heavy guns from the frontline. Kiev says it
cannot pull back as long as the rebels continue their advance.

Military trucks and tanks came and went in the largely
destroyed village of Nikishine as the rebels pounded nearby
Debaltseve with rockets, heavy artillery and mortar bombs.

"We'll take Debaltseve. It will all be ours. Our homeland
will remain our homeland," said a rebel tank operator who gave
his name only as Bass, his nom de guerre.

Observers from the OSCE security group, delegated to monitor
the ceasefire under last week's agreement, have been kept out of
Debaltseve by the rebels.

"We do not have the right (to stop fighting for Debaltseve).
It's even a moral thing. It's internal territory," said Denis
Pushilin, a senior separatist figure. The goal would be
"destroying the enemy's fighting positions".
(Additional reporting by Pavel Polityuk, Natalia Zinets,
Alessandra Prentice and Richard Balmforth in Kiev, Polina Devitt
in Moscow and Madeline Chambers in Berlin; Writing by Peter
Graff; Editing by Kevin Liffey)